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2 years ago

What is the value of y in the equation 4(5y –8 –2) = 185 –15?

1 answer:

8 0

In an equation the Left hand side must equal the right hand side 4(5y-8-2)=185-15 20y-32-8=170 20y=170+32+8 20y=210 Therefore y=10,5 When you substitute the 10,5 and solve it on the left and side it's equal to 170 which is the answer on the right hand side

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Solve for the variable in the following inequality 18 ≥ 6x

baherus [9]

Answer:

3 > x

Step-by-step explanation:

(Sorry if im wrong)

Divide both sides by 6

18/6 > 6x/6

3 > x

6 0

2 years ago

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

2 years ago

The figure below shows a shaded rectangular region inside a large rectangle:

pshichka [43]

Answer:

b. 58%

Step-by-step explanation:

Calculate the area of the entire rectangle using the formula A = lw.

The lowercase "L" is for length.

"w" is for width.

The lighter square is 10 units long by 5 inches wide.

A = lw

A = (10 in)(5 in) Multiply

A = 50 in²

Calculate the area for the shaded rectangle, 7 inches by 3 inches.

A = lw

A = (7 in)(3 in) Multiply

A = 21 in²

Calculate the area for the non-shaded region by subtracting the shaded area from the total area.

50 in² - 21 in² = 29 in²

The chance that a point in the large rectangle will NOT be in the shaded region is 29/50.

Convert this fraction to decimal form by using a calculator. Divide the top number by the bottom number.

29/50 = 0.58

0.58 is in decimal form. To convert it to a percentage, multiply the number by 100.

0.58 = 58%

Therefore the probability that a point chosen inside the large rectangle is not in the shaded region is 58%.

5 0

3 years ago

consider the four corners of the front wall of a rectangular class room (upper right, upper left, lower left, upper left) which

professor190 [17]

(You copied 'upper left' twice, and you left out 'lower right'.
But we know what you mean.)

If those are the corners of the wall, then they're ALL in the plane of
the wall (coplanar with it).

3 0

2 years ago

Please help me is this statement true or false 3(36 - 11) = 45?

viva [34]

Hi there! The answer is FALSE

To find the answer we need to work out the parenthesis.
$3(36 - 11) =$
$3 \times 36 - 3 \times 11 =$
$108 - 33 =$
$75$

75 does not equal 45 and therefore the statement is false.

3 0

3 years ago